Image-domain 4D-binning method and system

ABSTRACT

A method for increasing similarity between a base seismic survey and a monitor seismic survey of a same surveyed subsurface during a 4-dimensional (4D) project. The method includes receiving first seismic data associated with the base seismic survey; receiving second seismic data associated with the monitor seismic survey, wherein the monitor seismic survey is performed later in time than the base seismic survey; migrating the first and second seismic data to an image-domain; and calculating, with a processor, a set of decimating weights based on the migrated first and second seismic data in the image-domain, to maximize a similarity between the first seismic data and the second seismic data.

BACKGROUND

1. Technical Field

Embodiments of the subject matter disclosed herein generally relate tomethods and systems and, more particularly, to mechanisms and techniquesfor 4-dimensional (4D) binning seismic data collected with differentacquisition geometries.

2. Discussion of the Background

Marine seismic data acquisition and processing generate an image of ageophysical structure (subsurface) under the seafloor. While thisimage/profile does not provide a precise location for oil and gasreservoirs, it suggests, to those trained in the field, the presence orabsence of oil and/or gas reservoirs. Thus, providing a high-resolutionimage of the subsurface is an ongoing process for the exploration ofnatural resources, including, among others, oil and/or gas.

During a seismic gathering process, as shown in FIG. 1, a vessel 10 towsan array of seismic receivers 11 located on streamers 12. The streamersmay be disposed horizontally, i.e., lying at a constant depth relativeto the ocean surface 14, or may have spatial arrangements other thanhorizontal, e.g., variable-depth arrangement. The vessel 10 also tows aseismic source array 16 configured to generate a seismic wave 18. Theseismic wave 18 propagates downward, toward the seafloor 20, andpenetrates the seafloor until, eventually, a reflecting structure 22(reflector) reflects the seismic wave. The reflected seismic wave 24propagates upward until it is detected by receiver 11 on streamer 12.Based on this data, an image of the subsurface is generated.

Alternatively, ocean bottom cables (OBC) or ocean bottom nodes (OBN) andseismometers (OBS) may be used to record the seismic data. FIG. 2 showsan OBC 30 that includes plural receivers 32 distributed on the oceanbottom 20, which may be connected to each other (or may be independentOBN/OBS) with a cable 33 that may also be connected to a data collectionunit 34. Various means (e.g., underwater vehicle) may be used toretrieve the seismic data from the data collection unit 34 and bring iton the vessel 10 for processing.

One or more of the above-noted techniques may be used to monitor aproducing reservoir. For these instances, the goal of 4D processing isto determine how and where earth properties change by evaluatingdifferences in co-processed seismic data acquired at different times,usually before (i.e., the baseline survey) and after (i.e., the monitorsurvey) a period of fluid production from a petroleum reservoir.

Success of 4D processing depends on how well differences in acquisitionare compensated for during data processing and imaging. If thesedifferences are accurately compensated, changes in the subsurface thatare related to fluid production can be identified by areas ofsignificant difference between baseline and monitor images aftermigration. Failure of data processing to accurately compensate foracquisition differences leads to creation of 4D noise, which is anappreciable difference of baseline and monitor migrated images notcaused by fluid production and, thus, is unwanted.

A sensitive step of 4D processing is the selection of subsets of thebase and monitor data that have similar information content and similarwavefield sampling. If this similarity selection is accuratelyperformed, the level of 4D noise in the migrated images is much reduced.This data selection is commonly achieved by 4D-binning, as described inBrain et al., US Patent 20080170468 A1, and Zahibi et al. (2009,“Simultaneous multi-vintage 4D binning,” 71^(st) EAGE Conference andExhibition, Extended Abstracts), the contents of both documents beingincorporated herein by reference. Traditional 4D-binning selects tracesfrom the base and monitor surveys for further processing based on a setof criteria designed to assess their degree of similarity. All priorwork on this topic uses similarity criteria evaluated in the data domain(i.e., before migration).

For example, Brain et al. discloses a method for processing at least twosets of seismic data, each dataset comprising several seismic traces(i,j) grouped by bins (B_i, B_j) and by offset classes (O_i, O_j). Thismethod includes the following steps: calculating at least one attribute(a(i,j)) characteristic of a similarity between a first trace (i) of afirst dataset and a second trace (j) of a second dataset, and selectingor not the first and second traces (i,j) according to a selectioncriterion applied to the calculated attribute (a(i,j)).

This method explicitly groups the traces by bin and offset classes tofacilitate the 4D-binning process, which aims to decimate the baselineand monitor surveys to a common level of information and wavefieldsampling. The method described by Brain et al. and Zahibi et al. is nowwidely used in the geophysical industry, and assesses similarity of thetraces using surface attributes of the baseline and monitor surveys, forexample, the geographic position of traces defined by shot and receiverlocations, or by mid-point location and/or offset and/or azimuth.Alternative measures are also based on data-domain trace attributes suchas cross-correlation. In other words, traditional 4d-binning methods usea data-domain-related attribute (similarity) to group the traces.

The above-discussed 4D-binning processes work well when the baseline andmonitor surveys have similar acquisition geometry, for example, atowed-streamer base and a towed-streamer monitor acquired in similarpositions but at different times. However, when the base and monitorsurveys have different acquisition geometries, for example, atowed-streamer base and sparse OBN monitor, the surface or data-domaintrace attributes used to measure similarity in the 4D-binning processare not a good proxy for similarity of the data's information content,and/or of the wavefield sampling in the datasets.

Differences in both information content and wavefield sampling lead togeneration of 4D noise. Therefore, it is desirable to addressacquisition differences through more accurate methods of data decimation(more accurate methods for 4D-binning).

The problem of decimating two different datasets to a common level ofinformation and wavefield sampling is also addressed in U.S. Pat. No.8,339,898 (herein '898), the entire content of which is incorporatedherein by reference. The 4D-binning method described in '898 decimatesthe baseline and monitor data by evaluating similarity using a measurebased jointly on (i) interpolation to a common and regular surfacegeometry, and (ii) surface or data-domain trace attributes (as commonlyused in 4D-binning). More specifically, '898 discloses a method thatincludes, inter alia, computing measures associated with regularizationof the seismic data, and computing measures associated with 4D-binning,where the 4D-binning includes selecting traces from the seismic data oftime-lapse seismic surveys and discarding at least one trace of theseismic data that is based on considering both the regularizationmeasures and the 4D-binning measures.

The use of an interpolation engine to map data to a common and regulardata domain (with base and monitor traces occupying the same geographiclocations defined by their shot and receiver positions) facilitates the4D-binning process by providing a further measure of similarity.Interpolating to a common data domain would reduce the differences ofwavefield sampling, with differences in information content evaluated bythe simultaneous inclusion of surface or data-domain trace attributes inthe 4D-binning process.

However, where the baseline and monitor surveys have very differentacquisition geometry, such as towed-streamer base and sparse OBNmonitor, the interpolation of traces to a common surface data domaindoes not ensure common levels of wavefield sampling. Furthermore, theevaluation of similarity using surface or data-domain trace attributescannot accurately measure similarity of information content, since thegrouping of traces by surface attributes does not allow the comparisonof similar parts of the seismic wavefield.

The problem of matching two datasets with very different acquisitiongeometries is addressed in Provisional Patent Application 61/752,626(herein '626), “Wavefield modelling and 4D-binning for time-lapseprocessing of surveys from different acquisition datums,” the entiredisclosure of which is incorporated herein by reference. In '626,matching is addressed by the use of subsurface wavefield modeling. Thesubsurface modeling described in '626 uses ray-tracing to a targethorizon, with or without re-datuming of data to a more convenientgeometry, to define the subsurface reflection points and incidenceangles that should be matched in 4D-binning. The similarity measure usedin '626 is made after grouping traces by their subsurface properties(reflection points and incidence angles). Thus, the method incorporatesan estimate of subsurface reflection properties, but the subsurfacemodeling is limited to reflections on a target horizon. Furthermore,where a choice of trace pairs exists for a single estimated reflectionpoint and incidence angle, the similarity measures used to select tracesresorts to surface or data-domain trace attributes (albeit ones appliedto traces grouped by subsurface properties).

One weakness of the above-discussed 4D-binning methods is the relianceon grouping together of traces from the baseline and monitor prior toevaluating their similarity. Where the acquisition geometries ofbaseline and monitor are very similar and have similar positioning,these methods work well. However, the situation is different when theacquisition geometries are significantly different; trace grouping basedon surface attributes (such as offset or spatial trace bin) cannotensure that the right part of the monitor dataset is being compared withthe equivalent part of the baseline dataset. Where the subsurfacemodeling technique is used as described in '626, the trace grouping ismore accurate, but it still requires data-domain measures of similaritywhere a choice of traces exists.

Thus, there is a need for a new 4D-binning method that does not sufferfrom the limitations noted above.

SUMMARY

According to an exemplary embodiment, there is a method for increasingsimilarity between a base seismic survey and a monitor seismic survey ofa same surveyed subsurface during a 4-dimensional (4D) project. Themethod includes receiving first seismic data associated with the baseseismic survey; receiving second seismic data associated with themonitor seismic survey, wherein the monitor seismic survey is performedlater in time than the base seismic survey; migrating the first andsecond seismic data to an image-domain; and calculating, with aprocessor, a set of decimating weights based on the migrated first andsecond seismic data in the image-domain, to maximize a similaritybetween the first seismic data and the second seismic data.

According to another exemplary embodiment, there is a computing devicefor increasing similarity between a base seismic survey and a monitorseismic survey of a same surveyed subsurface during a 4-dimensional (4D)project. The computing device includes an interface configured toreceive first seismic data associated with the base seismic survey andsecond seismic data associated with the monitor seismic survey, whereinthe monitor seismic survey is performed later in time than the baseseismic survey; and a processor connected to the interface. Theprocessor is configured to migrate the first and second seismic data toan image-domain, and calculate a set of decimating weights based on themigrated first and second seismic data in the image-domain, to maximizea similarity between the first seismic data and the second seismic data.

According to still another embodiment, there is a non-transitorycomputer readable medium including computer executable instructions,wherein the instructions, when executed by a computer, implement themethod discussed above.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 is a schematic diagram of a conventional seismic data acquisitionsystem having plural seismic receivers on streamers;

FIG. 2 is a schematic diagram of a conventional seismic data acquisitionsystem having plural seismic receivers located at the ocean bottom;

FIG. 3 is a flowchart illustrating a novel method for 4D-binningaccording to an exemplary embodiment;

FIG. 4 is a flowchart illustrating a more detailed method for 4D-binningaccording to an exemplary embodiment;

FIG. 5 is a flowchart illustrating a step of the method for 4D-binningof FIG. 4 according to an exemplary embodiment;

FIG. 6 is a flowchart illustrating a method for 4D-binning according toan exemplary embodiment; and

FIG. 7 is a schematic diagram of a computing device for implementing theabove methods.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims. The following embodimentsare discussed, for simplicity, with regard to seismic data collectedduring a base survey and a monitor survey, wherein the base survey wasconducted with streamers and the monitor survey was conducted with oceanbottom nodes (OBNs). However, the embodiments to be discussed next arenot limited to these kinds of surveys. For example, the novelembodiments may be applied to a base survey conducted with OBNs and amonitor survey conducted with streamers. More generally, the novelembodiments are successful for base and monitor seismic surveys that mayhave different information content and/or wavefield sampling.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with an embodiment is included in at least oneembodiment of the subject matter disclosed. Thus, the appearance of thephrases “in one embodiment” or “in an embodiment” in various placesthroughout the specification is not necessarily referring to the sameembodiment. Further, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

According to an exemplary embodiment, a new method of matching twodatasets, in a 4D sense, is discussed. The novel method, asschematically illustrated in FIG. 3, uses a step 300 of data-domaindecimation strategy that is linked to a step 302 of using animage-domain similarity measure. This combination of (i) data-domaindecimation and (ii) image-domain similarity measure represents anadvance over the standard use of data-domain attributes in 4D-binning.Then, traditional processing is applied in step 304 (e.g., migration) onthe data binned as described in steps 300 and 302, and a final image ofthe surveyed subsurface is generated in step 306.

In this respect, as discussed above, similarity measures based ondata-domain attributes or trace grouping cannot accurately match tracesfrom very different acquisition geometries (e.g., towed-streamer andocean-bottom data). However, a more accurate match can be obtained byevaluating the need for decimation of baseline and monitor datasets inthe common migrated-image domain. This novel method, which is discussedin more detail next, is applicable in the 4D processing oftowed-streamer and ocean-bottom node datasets, or of other datasets withvery different acquisition geometries.

The novel method relies on linking the subsurface image (I) of baselineand monitor datasets to a set of decimating weights (w) which reduce theinput datasets (d) to a common level of information and wavefieldsampling. The decimating weights may be estimated by requiring theoutput images to be equal (e.g., in a least-squares sense, orequivalently with other minimizing norms) when using sections of theinput dataset known to correspond to stationary parts of Earth.Optionally, the estimating problem can be conditioned by requiring theset of decimating weights to have minimum gradient (thus, promotingsimilarity of weights for adjacent traces), or to have minimum totalmagnitude on the complementary set of weights (thus, maximizing the datathat survives the process and preventing the trivial solution of alldata being weighted to zero). In one application, the decimating weightsmay be determined as a function varying sample by sample, or varyingtrace by trace. In another application, no explicit grouping of tracesis required in the image-domain 4D-binning method.

The novel method is now discussed in more detail and based on a simpleexample. Consider a matrix A that holds, on its rows, coefficients of adiffraction-stack migration, or of a Kirchhoff migration (or any knownmigration). Those skilled in the art are familiar with these types ofmigrations and, for this reason, no details are provided about them. Thematrix (also called transform) A maps seismic data d onto a migratedimage I_(a). The transform A models a propagation of the wavefields inthe subsurface via ray-tracing through an arbitrary subsurface model.Coefficients in A's rows are placed such that multiplication of each rowof A with the data vector d achieves the Kirchhoff integral for aparticular image point (the image point is represented by the row of theimage vector I_(a)). Subscript a on the image vector indicates anevaluation of the image at a specific ensemble of points in the imagedomain that do not have to be regularly distributed. If subscript b isused to indicate the baseline survey, migration of this dataset can beexpressed as:I _(a|b) =A _(b) d _(b),  (1)where the data vector d_(b) is of dimensions (m×1), the image vectorI_(a|b) is of dimensions (p×1), and the migration matrix A_(b) is ofdimensions (p×m). Similarly, for the monitor (subscript m) the migrationof the corresponding dataset can be written as:I _(a|m) =A _(m) d _(m),  (2)where the data vector d_(m) is now (n×1), the image vector I_(a|m) isstill (p×1), and the migration matrix A_(m) is (p×n). In both cases, theimage is evaluated at the same position ensemble a in the image domain.

One feature of the novel method is to formulate a decimation strategythat makes use of migration engine A to evaluate the similarity of twovintages in the image domain. Use of a common image domain allows twovery different datasets to be accurately compared (e.g., towed-streamerand ocean-bottom data) without regard to differences in acquisitiongeometry, or other issues that make data-domain comparison difficult.For this reason, the novel method discussed herein overcomes thedifficulties associated with traditional methods discussed in theBackground section.

Next, consider a stationary part of the dataset, which should bereferred to in the following as a “training” dataset. For example, thetraining set could be chosen in a time window known to correspond withdata above the producing reservoir. A characteristic of the trainingdataset is that there is no 4D signal in it, so the migrated imagesshould be equal if the decimating weights are correct.

A set of decimating weights w_(b) and w_(m) are introduced, and thesedecimating weights should satisfy the following equations:I _(a|b) =A _(b) w _(b) d _(b)  (3)andI _(a|m) =A _(m) w _(m) d _(m),  (4)where the baseline weights w_(b) form a diagonal matrix of dimensions(m×m), and the monitor weights w_(m) form a diagonal matrix ofdimensions (n×n). Because these weights operate on the training dataset,then, if the decimating weights are correct, the following equalityholds I_(a|b)=I_(a|m).

Thus, an object of the method is to find, by optimization, the set ofdecimating weights that achieves this equality. To achieve this, it ispossible to concatenate (i) the data vectors d_(b) and d_(m) into asingle vector of length (m+n), and (ii) the weights matrices w_(b) andw_(m) into a diagonal matrix of dimensions ([m+n]×[m+n]). Then, inflatethe number of columns and zero-pad the migration matrices A_(b) andA_(m) such that the finite coefficients of the baseline migration areplaced in the first p rows and m columns of A′_(b), which is (p×[m+n]),and the finite coefficients of the monitor migration are placed in thefirst p rows and last n columns of A′_(m), which is also (p×[m+n]).Hence, equations (3) and (4) may be re-written as:I _(a|b) =A′ _(b) wd  (5)andI _(a|m) =A′ _(m) wd,  (6)where A′_(b)=[A_(b)|0_(b)] for a zero-matrix 0_(b) of dimensions (p×n),A′_(m)=[0_(m)|A_(m)] for a zero-matrix 0_(m) of dimensions (p×m),

${w = \begin{bmatrix}w_{b} & 0_{m}^{\prime} \\0_{b}^{\prime} & w_{m}\end{bmatrix}},$for zero-matrices 0′_(b) of dimensions (n×m) and 0′_(m) of dimensions(m×n), d=[d_(b) ^(T)|d_(m) ^(T)]^(T), and operation T means transpose.

Based on equations (5) and (6), a residuals vector r may be formed asfollows:r=I _(a|b) −I _(a|m) =A′ _(b) wd−A′ _(m) wd=(A′ _(b) −A′ _(m))wd.  (7)The set of decimating weights may be estimated by minimizing r^(T)r, orby use of some other norm (such as an L1-norm) to minimize theresiduals.

The set of decimating weights can be specified to take the valuesw=diag(w_(ii)=0,1) for i=1, . . . , m+n. The term diag(w_(ii)=0,1) meansthat the matrix is diagonal, so it has values only on the main diagonaland zeros everywhere else. The values that are on the main diagonal canbe either 0 or 1, depending on what produces the most similar image. Bya weight of 0, that part of the data is not included in the migration.By a weight of 1, the data is included. Other values are also possible,but would make the problem less well conditioned. Furthermore, theweights may be allowed to vary either sample by sample, or to takeblocks of values that represent the decimation of entire traces at atime.

The problem of estimating decimating weights by minimizing the residualsvector can be further conditioned by placing various regularizing termson the weights. For example, the trivial solution of matching twovintages by making all weights zero can be avoided by requiring the setof complementary weights {tilde over (w)}_(ii) to be {tilde over(w)}_(ii)=1,0 for w_(ii)=0,1, and to have minimum total magnitude {tildeover (w)}^(T){tilde over (w)}. Similarly, the weights may be required tobe flat (a minimum of the gradient of the weights), which promotesblocks of weights with similar values under the premise that adjacenttraces are likely to hold similar information content. Finally, acondition that requires even trace density may be added to promotequality of the 3D migrated image after the image-domain 4D-binning.

A few practical details associated with the novel method are nowdiscussed. In one application, the migration matrices are large, beingof dimensions (p×[m+n]) for p image points and m+n datapoints in thecombined baseline and monitor. Furthermore, the migration matrices arenon-sparse because they contain coefficients distributed over thedata-domain that includes Greens functions of the image points. Thus,the matrices may be too large to produce a solution of the entiredatasets in one pass. Nevertheless, by dividing the data intooverlapping spatio-temporal blocks, a set of weights may be obtained foreach block, and then it is possible to separately decimate the dataprior to a final migration.

Before the final migration takes place, further normalizing the data inthe overlap zones by their duplication number allows the final imagesfrom each block to be summed together. By dividing the data intooverlapping spatio-temporal blocks, one trace may be duplicated in theoverlap of q blocks. The duplication number for this trace is then q.The process may thus be parallelized in both the image domain (choosesmall p blocks) and in the data domain (choose small m, n blocks),although one of the domains needs to be large enough to contain themigration operator at a given aperture.

In one application, the migration represented by the migration matricesneed not be of the highest quality, because even something like adiffraction-stack migration provides a better domain in which toevaluate similarity of information content for decimation than the datadomain. Limiting the migration aperture is a cheap way to avoid aliasingon the image grid without having to filter the operator.

Having determined the set of decimating weights, these can be applied tothe data prior to a final migration using an imaging algorithm externalto the subsurface 4D-binning process.

Thus, the proposed image-domain 4D-binning method would improve the 4Dmatch between two surveys with very different acquisition geometries, inparticular for towed-streamer and ocean-bottom node data.

The proposed new method links data-domain decimation to similaritymeasures for the common migrated-image domain. In one application, thenovel method does not require explicit grouping of traces by spatial binand offset or angle class. In another application, the method does notrequire a similarity measure based on surface or data-domain traceattributes. Consequently, the method advantageously improves theaccuracy of 4D-binning when the input datasets have differentacquisition geometries.

According to an exemplary embodiment, discussed with regard to FIG. 4, a4D-binning algorithm includes the following steps. In step 400, 4Dseismic data is received. The 4D seismic data includes data from atleast two different 3D seismic surveys. In one application, one set ofseismic data has been collected with streamers while another set hasbeen collected with OBNs. In step 402, the 4D seismic data (i.e., thebaseline and monitor datasets) may be split into overlappingspatio-temporal blocks. The number of blocks may be one or more. In step404, the algorithm concatenates one block from each survey into aworking data vector d of length m+n for m datapoints in the baselineblock and n datapoints in the monitor block. Thus, plural data vectorsare formed as a result of this process. Next, the algorithm processeseach data vector separately. Considering the data vector d, thealgorithm advances to step 406, in which an ensemble of image points isdefined for the data vector. The ensemble of image points (associatedwith I_(a)) is defined so that the data vector d is mapped to it bymigration A. The image points may or may not be regularly distributed inthe image-domain. The ensemble of image points may be the same duringthe entire process or it may be chosen for each data block.

Next, a pre-defined velocity model is received in step 408. The velocitymodel describes the propagation speed of sound in water and subsurface,and this model may be obtained in many ways, as will be recognized bythose skilled in the art. Because determining a velocity model is beyondthe scope of this disclosure, no details are provided about the velocitymodel. Based on the velocity model, the algorithm calculates (e.g., byray tracing), in step 410, Green's functions of seismic waves thatpropagate from each image point in the ensemble to the position of eachsource and each receiver in the data vector. The source and receiverGreen's functions for each image point in the ensemble are combined instep 412 to define the coefficients of a Kirchhoff integral in acorresponding row of migration matrices A′_(b) and A′_(m). If anothermigration method is used, then a corresponding quantity is calculatedand not the Kirchhoff integral. Having the migration matrices A′_(b) andA′_(m), a net transform matrix A=A′_(b)−A′_(m) is formed. Next, based onthe net transform matrix A, the weights w are formed in step 416. Thisstep may include a number of substeps that are illustrated in FIG. 5. Instep 416, a vector of weights w=diag[w_(ii)] is formed for i=1, . . . ,m+n. In sub-step 416 a, the diagonal elements of the vector are set tobe one, i.e., w_(ii)=1. Then, in sub-step 416 b, the correspondingvector of complementary weights {tilde over (w)} is formed so that{tilde over (w)}=[{tilde over (w)}_(ii)=1,0] when w=[w_(ii)=0,1] andi=1, . . . , m+n. Note that the notation {tilde over (w)}_(ii)=1,0 meansa diagonal element of the vector w takes a value one or zero, and allother elements of the vector take a zero value. In sub-step 416 c, theresiduals vector r is calculated based on formula r=Awd. A cost functionE is defined in sub-step 416 d and then evaluated based on formulaE=r^(T)r+{tilde over (w)}^(T){tilde over (w)}. Note that additionalterms may be added to the cost function to promote, for example,flatness in the spatial trace density, or to improve the quality of the3D migrated images.

Cost function E is minimized with respect to the set of weights insub-step 416 e, using various mathematical methods. For example,minimization of the cost function may be achieved using the method ofconjugate gradients applied to the vector of weights w. The algorithmmay loop back in sub-step 416 f to sub-step 416 b (note that the set ofweights may be varied at each step and thus, complementary weights needto be re-calculated in each step) until the cost function is minimized.Once the cost function has been minimized, the vector of weights thatminimizes the cost function for the given data d is obtained. Then, thealgorithm returns to step 406 to address the next vector of data untilall data is processed.

Returning to FIG. 4, the vector of weights w for the entire data d ismultiplied in step 418 by the vector of data d and then, in step 420,the weighted data vector is split back into the spatio-temporal blocksof step 402. From step 420, the algorithm advances to step 422, in whichdata may be normalized in the overlap zones of the blocks by theirduplication number. After one or more processing steps, the final imageof the surveyed subsurface is generated in step 424.

According to an exemplary embodiment illustrated in FIG. 6, there is amethod for increasing a similarity between a base seismic survey and amonitor seismic survey of a same surveyed subsurface during a4-dimensional (4D) project. The method includes a step 600 of receivingfirst seismic data associated with the base seismic survey; a step 602of receiving second seismic data associated with the monitor seismicsurvey, wherein the monitor seismic survey is performed later in timethan the base seismic survey; a step 604 of migrating the first andsecond seismic data to an image-domain; and a step 606 of calculating,with a processor, a vector of decimating weights based on the migratedfirst and second seismic data in the image-domain to maximize asimilarity between the first seismic data and the second seismic data.

An example of a representative computing device capable of carrying outoperations in accordance with the exemplary embodiments discussed aboveis illustrated in FIG. 7. Hardware, firmware, software or a combinationthereof may be used to perform the various steps and operationsdescribed herein.

The exemplary computer device 700 suitable for performing the activitiesdescribed in the exemplary embodiments may include server 701. Such aserver 701 may include a central processor unit (CPU) 702 coupled to arandom access memory (RAM) 704 and to a read-only memory (ROM) 706. ROM706 may also be other types of storage media to store programs, such asprogrammable ROM (PROM), erasable PROM (EPROM), etc. Processor 702 maycommunicate with other internal and external components throughinput/output (I/O) circuitry 708 and bussing 710 to provide controlsignals and the like. Processor 702 carries out a variety of functionsas are known in the art, as dictated by software and/or firmwareinstructions.

Server 701 may also include one or more data storage devices, includinghard disk drives 712, CD-ROM drives 714, and other hardware capable ofreading and/or storing information such as a DVD, etc. In oneembodiment, software for carrying out the above-discussed steps may bestored and distributed on a CD-ROM or DVD 716, removable media 718 orother forms of media capable of portably storing information. Thesestorage media may be inserted into, and read by, devices such as theCD-ROM drive 714, the drive 712, etc. Server 701 may be coupled to adisplay 720, which may be any type of known display or presentationscreen, such as LCD or LED displays, plasma displays, cathode ray tubes(CRT), etc. A user input interface 722 is provided, including one ormore user interface mechanisms such as a mouse, keyboard, microphone,touch pad, touch screen, voice-recognition system, etc.

Server 701 may be coupled to other computing devices via a network. Theserver may be part of a larger network configuration as in a global areanetwork (GAN) such as the Internet 728.

As also will be appreciated by one skilled in the art, the exemplaryembodiments may be embodied in a wireless communication device, atelecommunication network, as a method or in a computer program product.Accordingly, the exemplary embodiments may take the form of an entirelyhardware embodiment or an embodiment combining hardware and softwareaspects. Further, the exemplary embodiments may take the form of acomputer program product stored on a computer-readable storage mediumhaving computer-readable instructions embodied in the medium. Anysuitable computer-readable medium may be utilized, including hard disks,CD-ROMs, digital versatile discs (DVD), optical storage devices, ormagnetic storage devices such as floppy disk or magnetic tape. Othernon-limiting examples of computer-readable media include flash-typememories or other known types of memories.

The disclosed exemplary embodiments provide an apparatus and a methodfor increasing a similarity between base and monitor surveys in a 4Dproject by data-domain decimation implemented using image-domainmeasures of similarity. It should be understood that this description isnot intended to limit the invention. On the contrary, the exemplaryembodiments are intended to cover alternatives, modifications andequivalents, which are included in the spirit and scope of the inventionas defined by the appended claims. Further, in the detailed descriptionof the exemplary embodiments, numerous specific details are set forth inorder to provide a comprehensive understanding of the claimed invention.However, one skilled in the art would understand that variousembodiments may be practiced without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone without the other features andelements of the embodiments or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

What is claimed is:
 1. A method for increasing similarity between a base seismic survey and a monitor seismic survey of a same surveyed subsurface during a 4-dimensional (4D) project, the method comprising: receiving first seismic data associated with the base seismic survey; receiving second seismic data associated with the monitor seismic survey, wherein the monitor seismic survey is performed later in time than the base seismic survey; migrating the first and second seismic data to an image-domain; and calculating, with a processor, a set of decimating weights based on the migrated first and second seismic data in the image-domain, to maximize a similarity between the first seismic data and the second seismic data.
 2. The method of claim 1, further comprising: applying the decimated weights to the first and second seismic data; and generating an image of the surveyed subsurface based on the decimated weights and the first and second seismic data.
 3. The method of claim 1, further comprising: splitting the first and second seismic data into overlapping spatio-temporal blocks; and concatenating data corresponding to pairs of blocks from each of the first and second seismic data blocks to form a data vector.
 4. The method of claim 3, further comprising: defining an ensemble of image points in the image-domain.
 5. The method of claim 4, further comprising: calculating a first migration matrix for the first seismic data and a second migration matrix for the second seismic data.
 6. The method of claim 5, wherein an element of the first or second migration matrix is calculated based on Green functions that describe propagations (i) of a seismic wave from a seismic source to a point of the ensemble of image points and (ii) of a seismic wave from a seismic receiver to the point of the ensemble of points.
 7. The method of claim 5, further comprising: combining the first and second migration matrices to obtain a net migration matrix.
 8. The method of claim 7, further comprising: forming a vector of weights that have only diagonal elements equals to zero or one; and calculating a residuals vector based on the net migration matrix, the vector of weights, and the data vector.
 9. The method of claim 8, further comprising: defining a cost function based on the residuals vector and the vector of weights; and minimizing the cost function to obtain the decimating data weights.
 10. The method of claim 9, further comprising: multiplying the data vector with the decimating data weights to obtained weighted data.
 11. The method of claim 10, further comprising: splitting the weighted data back into the spatio-temporal blocks.
 12. The method of claim 11, further comprising: normalizing the weighted data by corresponding duplication numbers; and writing a block number to a header of each data trace of the first and second seismic data.
 13. The method of claim 1, wherein one of the base and monitor surveys is a streamer based survey and the other of the base and monitor surveys is an ocean bottom node survey.
 14. A computing device for increasing similarity between a base seismic survey and a monitor seismic survey of a same surveyed subsurface during a 4-dimensional (4D) project, the computing device comprising: an interface configured to receive first seismic data associated with the base seismic survey and second seismic data associated with the monitor seismic survey, wherein the monitor seismic survey is performed later in time than the base seismic survey; and a processor connected to the interface and configured to, migrate the first and second seismic data to an image-domain, and calculate a set of decimating weights based on the migrated first and second seismic data in the image-domain, to maximize a similarity between the first seismic data and the second seismic data.
 15. The computing device of claim 14, wherein the processor is further configured to: apply the decimated weights to the first and second seismic data; and generate an image of the surveyed subsurface based on the decimated weights and the first and second seismic data.
 16. The computing device of claim 14, wherein the processor is further configured to: split the first and second seismic data into overlapping spatio-temporal blocks; and concatenate data corresponding to pairs of blocks from each of the first and second seismic data blocks to form a data vector.
 17. The computing device of claim 16, wherein the processor is further configured to: define an ensemble of image points in the image-domain, calculate a first migration matrix for the first seismic data and a second migration matrix for the second seismic data, combine the first and second migration matrices to obtain a net migration matrix, form a vector of weights that have only diagonal elements equals to zero or one, and calculate a residuals vector based on the net migration matrix, the vector of weights, and the data vector.
 18. The computing device of claim 17, wherein the processor is further configured to: define a cost function based on the residuals vector and the vector of weights, minimize the cost function to obtain the decimating data weights, multiply the data vector with the decimating data weights to obtained weighted data, split the weighted data back into the spatio-temporal blocks, and normalize the weighted data by corresponding duplication numbers.
 19. The computing device of claim 14, wherein one of the base and monitor surveys is a streamer based survey and the other of the base and monitor surveys is an ocean bottom node survey.
 20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement a method for increasing similarity between a base seismic survey and a monitor seismic survey of a same surveyed subsurface during a 4-dimensional (4D) project, the method comprising: receiving first seismic data associated with the base seismic survey; receiving second seismic data associated with the monitor seismic survey, wherein the monitor seismic survey is performed later in time than the base seismic survey; migrating the first and second seismic data to an image-domain; and calculating, with a processor, a set of decimating weights based on the migrated first and second seismic data in the image-domain, to maximize a similarity between the first seismic data and the second seismic data. 